I'm trying to figure out what the Livonian character ȱ sounds like. As far as I can tell, it's a long mid-high unrounded back vowel. In IPA it seems to be written as
/ɤː/ but that seems to be a non-standard IPA form?
The symbol [ɤː] is the correct one for the sound you describe and is a standard IPA symbol (although it's not a super-common vowel in the world's languages, but does crop up here and there).
There is also the near-high (as opposed to high-mid) back rounded vowel [ʊ]; perhaps this is what you were expecting?
As for what these sound like, have a look at this website: http://www.ipachart.com/.